The collapse of the ruble has prompted a flight of capital as investors and savers in Russia seek shelter outside the country's borders.

A CNBC.com analysis of money flows monitored by the Russian Central Bank shows that large cash hoards have already left the country. Nations in the ex-Soviet Commonwealth of Independent States (CIS) have been disproportionate recipients of those funds. Ukraine is also a major destination for Russian cash.

Since 2006, the earliest data available, Russian individuals have sent nearly $200 billion out of the country—or more than 10 percent of the country's gross domestic product for 2013.

Russian central bankers have been frantically trying to stem a further collapse of the national currency, including a surprise move this week to jack up interest rates to 17 percent. The hope is that those higher rates will bring more hard cash back into Russia—or keep it from leaving.

But the data show that Russians have been sending their money outside the country for years. And the flow of cash has accelerated in the last year, up from $5.9 billion in the first quarter of 2013 to $13.4 billion in the third quarter of this year, the latest data available.

The crash in Russia's currency has closely tracked the price of oil—which is the lifeblood of the Russian economy. Both have fallen by nearly half since July, and there is little certainty about where oil prices will stabilize.

Steep losses in oil revenues are expected to drag the Russian economy into recession next year, and the ruble's lost value will sharply raise the cost of imported goods the Russian economy depends on.

Read MoreLame duck? Obama comes on strong after midterms

The hike in interest rates to shore up the ruble will also create a steep headwind for economic growth.

"The devastating consequences that the current oil price will have on Russia's economy and its financial system suggest calm may not be restored anytime soon, keeping the ruble under pressure," John Higgins, chief markets economist at Capital Economics, said in a recent note to clients.

Russian President Valdimir Putin, at a news conference Thursday, expressed confidence that the measures in place will eventually reverse the ruble's plunge.

"If the situation develops unfavorably, we will have to amend our plans. Beyond doubt, we will have to cut some (spending). But a positive turn and emergence from the current situation are inevitable," Putin said.

"The growth of the global economy will continue, and our economy will rebound from the current situation," he said, sitting at a large desk before a studio audience, with his comments broadcast live to the nation.

But Russians have less confidence in the outlook for the ruble, based on the flows of cash outside the country. One of the most popular destinations is Switzerland, whose currency and banking system have long been regarded as a safe haven in times of financial turmoil.

Demand for Swiss francs has soared so much, in fact, that the Swiss National Bank has begun charging commercial banks to park their currency by imposing negative interest rates.